Concepts of ferrovalley material and anomalous valley Hall effect

Valleytronics rooted in the valley degree of freedom is of both theoretical and technological importance as it offers additional opportunities for information storage, as well as electronic, magnetic and optical switches. In analogy to ferroelectric materials with spontaneous charge polarization, or ferromagnetic materials with spontaneous spin polarization, here we introduce a new member of ferroic family, that is, a ferrovalley material with spontaneous valley polarization. Combining a two-band k·p model with first-principles calculations, we show that 2H-VSe2 monolayer, where the spin–orbit coupling coexists with the intrinsic exchange interaction of transition-metal d electrons, is such a room-temperature ferrovalley material. We further predict that such system could demonstrate many distinctive properties, for example, chirality-dependent optical band gap and, more interestingly, anomalous valley Hall effect. On account of the latter, functional devices based on ferrovalley materials, such as valley-based nonvolatile random access memory and valley filter, are contemplated for valleytronic applications.


5)
Authors should provide more examples that only the 2H-VSe2 monolayer: in similar materials, the strong hybridization with the p states of the chalcogen atom could play a fundamental role in the proposed valleytronic effects. In this respect, authors should show the atom-projected density of states and discuss what is the role of the d-p hybridization, and if it is significant. I would expect that their conclusion would be quite different for systems like WSe2, where the wider spread of the d-like electronic density of the transition metal would produce a higher hybridization with the p orbitals of the chalcogen atom, the latter thus playing a fundamental role in the proposed valleytronic effects. 6) As a personal suggestion, when authors opt for the "double blind" peer review option, they should remove or modify any sentence in the manuscript that could unveil authors' identity, as suggested in Nature authors' guidelines. For example, in the method section, they say "For the optical property calculations, we adopt our own code OPTICPACK..." providing the reference. Furthermore, if authors want to preserve their anonimity during the peer review process, they should not upload the full version in the arXiv server (see https://arxiv.org/abs/1604.05833).
I am very happy with the revision of the manuscript. I think my questions, partially due to fast reading, have improved the presentation a bit.
I would just like the authors to add a little discussion about their material. They write now that two layered phases (T and H) should exist, but a little more information to the reader who is unfamiliar with VSe2 is needed. The discussion should include (i) stability, in particular inbetween the phases (see e.g. the reference to Zhongfang Chen's work), (ii) potential availability -I found some references to experimental VSe2, though not to 2H VSe2 (possibly due to lack of resources as I am travelling).
Thus, after this point is addressed (minor revision) I recommend acceptance.
Reviewer #3 (Remarks to the Author): I went through the revised version of the manuscript and I believe that authors made their best effort to answer the reviewers' questions. The work is improved and properly justified. However, a direct experimental application of their formulation is lacking. Despite authors provided examples in their response, those are not quantitative and not directly tied with the quantities present in their formulation. For this reason I cannot still recommend the publication of their work in Nature Communications. Nevertheless, the power of their method and the immediate interest of other experimental groups demonstrate the importance of authors' work. As a such, I renew my suggestion to submit their work to other journals like Physical Review B, or similar; if authors are able to prove more extensively the general result of their work, I also suggest to submit their manuscript to journal of wider audience like Scientific Report.
VSe2 and its magnetism has been subject to quite a few theoretical studies (e.g. doi: 10.1063/1.4893027, 10.1088/0953-8984/28/6/064002, 10.1016/j.jssc.2013.03.008, 10.1021/nn204667z). The Hall effect has been reported in a sandwich structure incorporating VSe2 (10.1557VSe2 (10. /jmr.2015. The idea of applying an electric field to manipulate the split valleys was, for example, reviewed here: 10.1039/c4cs00276h. The combination of the anomalous Hall effect with the magnetism of the system has not been discussed before. The question is if this is such surprising result to merit a Nature Comm., or is this incremental. In particular, is the Hall effect of the same origin as the one published in the sandwich (10.1557/jmr.2015.354). This requires more analysis and discussion.
While, "under consideration of spin-orbit coupling and" the intrinsic exchange interaction of transition-metal-d electrons, we propose a way to explore spontaneous valley polarization in our work. As a semiconductor with both the SOC effect and "strong magnetic coupling", 2H-VSe 2 is a certain material, possessing spontaneous valley polarization independent on any external fields, which is so-called a ferrovalley material.
Due to the advantage of nonvolatility, our strategy is apparently distinct from "the idea of applying an electric/magnetic field to manipulate the split valleys" reviewed in the paper you recommended "The electronic structure calculations of two-dimensional transition-metal dichalcogenides in the presence of external electric and magnetic fields" (doi: 10.1039/c4cs00276h), as well as some other volatile approaches utilizing external fields including force and optical ones. In fact, the spontaneous valley polarization in the absence of any external fields is exactly the hightlight of our work. It implies the potential application of ferrovalley materials in nonvolatile data storage and other nextgeneration electronic products. In analogy to ferroelectric materials with spontaneous charge polarization in electronics, as well as ferromagnetic materials with spontaneous spin polarization in spintronics, the concept of "ferrovalley material" with spontaneous valley polarization is a new member of ferroic-family, and is of both fundamentally physical and practically technological importance in ferroic and valleytronic fields.
In addition, we respectfully point out that most of the papers you recommended (doi: 10. 1063/1.4893027, 10.1016/j.jssc.2013.03.008, 10.1021/nn204667z, and 10.1557/jmr.2015.354) focused on 1T-phase VSe 2 . Fig. 1(a) in "Evidence of the existence of magnetism in pristine VX 2 monolayers (X = S, Se) and their strain-induced tunable magnetic properties" (doi: 10.1021/nn204667z), the right panel of Fig. 1  In order to clearly demonstrate the difference of VSe 2 between the 1T-and 2H-phase and avoid possible misunderstanding, the sentence "Noted that the pristine 1T-phase VSe 2 has been widely studied [37][38][39][40] . However, with the presence of space inversion symmetry, it is not a ferrovalley material." has been added in the first paragraph of the subsection "Chirality-dependent optical band gap and Berry curvatures in the ferrovalley material". Answer: We apologize that the main text of our previous manuscript was not divided appropriately. According to your suggestion and the "Guide to authors" of Nature Communications, we seriously analyze the structure of the main text. Now, it is reorganized in the revised version. The origin subsection "Anomalous valley Hall effect" now becomes "Discussion". The concluding paragraph is removed, whose contents accordingly transfer to proper places in the main text. More details are available in the "Summary of Changes" (see below). We believe that the sections headed "Results" and "Discussion" in the resubmitted manuscript are really separated this time.
Scientifically the paper appears to be sound and everything is well justified.
Answer: We sincerely thank you for your positive comment of our work.
I believe the strong point of the paper (which is beyond Figure 2)  Answer: Following your suggestions, results and discussion sections have been already really separated. All the references you recommended have been cited in our revised manuscript, as summarized in the "Summary of Changes" (see below).
As displayed in Fig  The results and the new properties appear to be well discussed and justified. Therefore I'm in favor for publication of this work in Nat. Comm.
Answer: We thank you very much for your appreciation of our work, especially your positive recommendation and helpful advice. All the issues are addressed in the following paragraphs.
1. the English should be improved; I would avoid terms like "star of outlook", "following the tactic", and similar.
Answer: The phrases are corrected in our revised manuscript. "the star of outlook" is changed to "the most promising ones". "following the tactic" is replaced by "following the strategy" . Some other long sentences and expressions not proper of the standard scientific English are also corrected, as summarized in the "Summary of Changes" (see below).

row 39: remove--->removed!?
Answer: The sentence "When the applied external fields including force, electric, magnetic and optical ones remove …" is corrected as "When the applied external fields including force, electric, magnetic and optical ones are removed…".

row 124: declaring!?
Answer: The sentence "…declaring that it could be used in valleytronics well above room temperature." is changed to "It demonstrates that 2H-VSe 2 monolayer could be used in valleytronics well above room temperature.".

row 127: thankfully!?
Answer: The sentence "Thankfully, the intrinsic exchange interaction of unpaired d electrons,…" is replaced by "Fortunately, the intrinsic exchange interaction of unpaired d electrons,…".

row 179: inversed (reverted)
Answer: We think the word "reversed" is more appropriate to be used here. So the sentence "Not surprisingly, same value with opposite sign is obtained when the valley polarization has been inversed (Fig. 4d)." is corrected as "Not surprisingly, same value with opposite sign is obtained when the valley polarization has been reversed (Fig. 4d).".
In addition, the word "inversed" of the sentence "Amazingly, inversed chirality of the incident light sees different…" in the last paragraph of the subsection "Valley-dependent optical selection rule based on group theory analysis" is also replaced by "reversed".

row 213: Discussion-->Conclusion.
Answer: We are sorry to point out that the section headed Conclusion seems unable to be included according to the "Guide to authors" of nature communications. As mentioned by the Reviewer #1, the main text of our previous manuscript was not divided appropriately.
In the revised version, it is reorganized.

Authors propose the concept of "ferrovalley material" and "anomalous valley Hall effect"
within the context of functional devices based on valleytronic effects. The manuscript is not easy to read due to the English form, that should be revised and checked for typos, long sentences and expressions not proper of the standard scientific English.
Answer: We apologize to bother you with the English form. We have carefully checked our manuscript, and tried our best to avoid typos, improper long sentences and expressions in the revised version. For example, the phrase "the star of outlook" is changed to "the most promising ones". The long sentence "Particularly, the noncentrosymmetry together with intrinsic spin-orbit coupling (SOC) originated from the d-orbitals of heavy transition metals induce strong coupled spin and valley degree of freedom, making them as a promising platform for the study of the fundamental physics in spintronics, valleytronics and crossing areas." is divided into "Particularly, the noncentrosymmetry together with intrinsic spin-orbit coupling (SOC) derived from the d-  As we know, the exchange interaction, equivalent to an intrinsic magnetic field, tends to split the spin-majority and spin-minority states. In the case, if the degeneracy between K + and Kvalleys in TMDs monolayers can be broken by an external magnetic field, our strategy must be effectively. As mentioned in the section "Introduction" of our  Fig. R3), while the exchange interaction in VSe 2 corresponds to the magnetic coupling between V-3d orbitals. Therefore, a similar ferromagnetic character is very likely to be found in 2H-VSe 2 as its 1T-phase possesses. Overall, the experimental results mentioned above are powerful evidences to prove the feasibility of our findings. In fact, related attempts are carrying out by our experimental partners. When we realized our manuscript on arXiv, several theoretical and experimental groups, such as F. Zhang's group in the University of Texas at Dallas and C. S. Tian's group in Fudan University, contacted with us and expressed their interests. We are confident that our findings will be supported by experimental work in the near future.
Nevertheless, considering that our work are "a significant advance" in the highly competitive valleytronic field, we hope it can be published in Nature Communications as soon as possible, even in the absence of directly experimental data currently. Our study, which is of both fundamentally physical and practically technological importance in spintronics, valleytronics and crossing areas, will certainly appeal to a broader audience of Nature Communications and drive experimental efforts on monolayer 2H-VSe 2 and other 2H-phase V-group dichalcogenides, where a series of ferrovalley materials are very likely to hide.
Other issues you pointed out are addressed in the following paragraphs. Following your suggestions, the choice of the PBE functional is justified as "The exchange-correlation potential is treated in Perdew-Burke-Ernzerhof (PBE) form 48 of the generalized gradient approximation (GGA) with a kinetic-energy cutoff of 600 eV, as others did 34-36 . We also check that our results are qualitatively robust within the Ceperly-Alder functional form of the local density approximation (LDA) and taking the Hubbard U into account to describe the on-site Coulomb repulsion between V-d electrons". The kmesh used to sample the Brillouin zone is now stated in our revised manuscript as "A 18×18×1 and 36×36×1 Monkhorst-Pack k-point mesh centered at Γ are respectively adopted in the geometry optimization and self-consistent calculations.". In addition, the meaning of the variables W k , v and c in equation 6, which was not demonstrated in the previous version, is clearly explained as "The integral over the k space has been replaced by a summation over special k points with corresponding weighting factor W k . The second summation includes v and c states, based on the reasonable assumption that the VB is fully occupied, while the CB is empty.".

2) Line 16-18: authors speak suddenly about an effect specific of the hexagonal symmetry without introducing why this is needed. They mention in the abstract that the study will focus on 2H-VSe2 that has hexagonal symmetry but this should be properly introduced in the main text for the sake of fluency and clarity of the arguments discussed in the introductory paragraph.
Answer: From the perspective of valleytronics, the hexagonal symmetry is not necessary.

3) Line 23, "the space inversion symmetry for these 2D materials are explicitly broken":
if I understood the grammar mistake correctly, I guess authors refer to the fact that the inversion symmetry is broken in monolayers with respect to the bulk counterpart, but this should be explicitly said.
Answer: We apologize for the misunderstanding here. We refer to the fact that unlike graphene with space inversion symmetry, inversion symmetry is explicitly broken in these TMDs monolayers. As known to all, in graphene, the unit cell consists of two carbon atoms, i.e. the A and B sublattices. However, the equivalence between the two sublattices makes graphene centrosymmetric. In order to induce band gap and make practical use of valley index, various approaches have been adopted to break the inversion symmetry in graphene, such as epitaxial engineering (Nat. Mater. 6, 770 Fortunately, in pristine 2H-TMDs monolayers, the inversion symmetry is intrinsically broken, leading to intriguing phenomena and the possibility to utilize and manipulate valley degree of freedom directly. According to your suggestion, the sentence is now corrected as "With respect to centrosymmetric graphene, the space inversion symmetry for these 2H-phase TMDs is explicitly broken, which gives rise to the existence of the valley Hall effect, as well as the valley-dependent optical selection rules." 4) Line 89. "While for K...changes as 1E'": sentence is not complete, thus not clear.
Answer: The sentence "While for K -, the one for the bottom of the UB changes as 1E′." is replaced by "While for K -, they become A′ and 1E′. It is obvious that the IRs for the bottom of UB are different between the two valleys." in the reversed manuscript. We think it clearly demonstrates the symmetry for LB and UB at valley K -, which is schematically displayed in Fig. 1a.  Rev. Lett. 108, 196802 (2012).).

5) Authors should provide more examples that only the 2H-
The fact is clearly reflected in the two-band k·p model we adopted. As mentioned in our  Since you are quite interested in the hybridization, we are pleased to compare the atomprojected band structures among WSe 2 , VSe 2 without ferromagnetism and VSe 2 in real case here. No matter for the WSe 2 ( Fig. R4(a)) and the VSe 2 without ferromagnetism ( Fig.   R4(b)), the bottom of the conduction bands in two valleys dominantly consist from d z 2 orbitals on transition metals. At the top of the valance bands, there exist mainly d x 2 -y 2 and d xy states of cations. The occupations of Se-p states are far beyond the valleys K + and K -.
Not surprisingly, the energetically degenerated bands between valleys prove that WSe 2 is merely a paravalley material. Because the exchange interaction, or equivalently magnetism, is not taken into account, the ferrovalley character for VSe 2 does not appear.
For VSe 2 in real case (Fig. R4(c)), the coexistence between the SOC effect and ferromagnetism splits valley degeneracy, stabilizing the system in ferrovalley state.
Although, the dispersion of band structures is quite different from the one excluding magnetism, the hybridization between V-d and Se-p states around the valleys is still negligible.
The atom-projected band structures clearly demonstrate that the electronic behavior near the valleys can be described by the basis functions |ψ τ u > = |d z 2> and |ψ τ l > = (|d x 2 -y 2> + iτ|d xy >) / 2 (τ = ±1 denotes the valley index). Their hybridization with the p orbitals of the chalcogen atom can be excluded. More importantly, they imply that the coexistence of the SOC effect and exchange interaction of localized d-electrons is the sufficient condition for valley polarization.
Considering that the hybridization is not the key issue of our work, we do not insert the Fig. R4 into our manuscript. We think the sentence "When we ignore the magnetism in monolayer 2H-VSe 2 , as shown in Fig. 2a, the band structure is essentially similar to the representative one for TMDs (Fig. 1b)." is strong enough to describe the case. However, if you insist that the figure is necessary, we are also glad to add it.

6) As a personal suggestion, when authors opt for the "double blind" peer review option, they should remove or modify any sentence in the manuscript that could unveil authors'
identity, as suggested in Nature authors' guidelines. For example, in the method section, they say "For the optical property calculations, we adopt our own code OPTICPACK..." providing the reference. Furthermore, if authors want to preserve their anonimity during the peer review process, they should not upload the full version in the arXiv server (see https://arxiv.org/abs/1604.05833).
Answer: The intention to choose the "double blind" peer review option is just for our "curiosity". Frankly speaking, Nature Communications is the first journal we are aware of providing such option. So, we are willing to be "the first person to try tomato". As a green hand, we appear to be clumsy and accidentally unveil our identity. However, scientific researches are always continuous. When we introduce the "Method" we adopted during our first-principles calculations, it seems to be inevitable to describe our own code OPTICPACK and then cite corresponding references. Anyway, we apologize for our negligence.
As you can understand, valleytronics is now one of the hottest and most competitive field among condensed matter physics. We are confident that our work is of both fundamentally physical and practically technological importance in this field, as well as some other areas, such as multiferroicity and Hall effects. In order to preserve our credit and broadcast our interesting findings to advocate further research on ferrovalley materials, we upload the full version in the arXiv server in advance. As mentioned above, several experimental groups contacted with us and expressed their interests. The data (http://adsabs.harvard.edu/cgi-bin/nph-ref_history?refs=AR&bibcode=2016arXiv160405833T) from "Reads History" also shows that a broader audience has already been appealed in a very short time. Certainly, the influence of excellent journals like Nature Communications is far beyond it. Therefore, we hope it can be published in Nature Communications as soon as possible.
Following your suggestions, we have tired our best to seriously revise the current manuscript. Hope our earnest responses, listed above, appropriately answer all your concerns, especially the experimental ones, and make you willing to change the decision.  2. The origin subsection "Anomalous valley Hall effect" now becomes "Discussion".

Summary of Changes
The concluding paragraph is removed. The sentence "As a new ferroic-family member, its potential coupling with ferroelectric, ferromagnetic, ferroelastic and ferrotoroidic properties may provide novel physics in multiferroic field and promote technological innovation." has been moved to the fourth paragraph of the main text.
The sentence "We strongly advocate experimental efforts on monolayer 2H-VSe 2 and other 2H-phase V-group dichalcogenides, where a series of ferrovalley materials are very likely to hide. It is of great importance in paving the way to the practical applications of valleytronics." has been transferred to the fourth paragraph of the section "Discussion".
3. The sentence "With the celebrated discovery of graphene 1 , the concept of valleytronics based on graphene-related materials (GRMs) with honeycomb lattice symmetry has attracted immense attention 2-5 ." has been corrected as "With the discovery of graphene 1 , the concept of valleytronics has attracted immense attention 2,3 .". 4. The sentence "Similar to charge and spin of electrons in electronics and spintronics, the valley degree of freedom in the field of valleytronics, corresponding to degenerate but unequivalent K + and Kpoints (so called valleys) at the corners of the twodimensional (2D) hexagonal Brillouin zone, constitutes the binary states." has been simplified as "Similar to charge and spin of electrons in electronics and spintronics, the valley degree of freedom in the field of valleytronics constitutes the binary states.". 5. "GRMs" and "star of outlook" in the first sentence of the second paragraph have been changed to "valleytronic materials" and "most promising ones".
6. The sentence "At variance with graphene, the space inversion symmetry for these 2D materials are explicitly broken, which gives rise to the existence of the valley Hall effect 4 , as well as the valley-dependent optical selection rules 11 ." has been replaced by "With respect to centrosymmetric graphene, the space inversion symmetry for these 2H-phase TMDs is explicitly broken, which gives rise to the existence of the valley Hall effect 4 , as well as the valley-dependent optical selection rules 11 .". 7. The sentence "Particularly, the noncentrosymmetry together with intrinsic spin-orbit coupling (SOC) originated from the d-orbitals of heavy transition metals 11 induce strong coupled spin and valley degree of freedom, making them as a promising platform for the study of the fundamental physics in spintronics, valleytronics and crossing areas." has been divided into "Particularly, the noncentrosymmetry together with intrinsic spin-orbit coupling (SOC) derived from the d-orbitals of heavy transition metals 12 induce strong coupled spin and valley degree of freedom.
Therefore, 2H-TMDs monolayers are generally regarded as the promising platform for studies of the fundamental physics in spintronics, valleytronics and crossing areas.". 8. The sentence "In analogy with paraelectric and paramagnetic materials, the pristine TMDs monolayers are not suitable for long-term storing information." Has been rewritten as "The pristine TMDs monolayers, however, are not suitable for direct information storage, as the valleys in these systems are not polarized. In analogy to paraelectric and paramagnetic materials, they can be called paravalley materials.". 9. The word "unaccessible" in the sentence "Unfortunately, the extreme field strength for a sizable valley splitting is unaccessible in practical use." has been corrected as "not accessible".
10. The gramma mistake in the sentence "When the applied external fields including force, electric, magnetic and optical ones remove, the valleys locked by time-reversal symmetry are still degenerate, stabilizing the system in the initial paravalley state." Has been corrected. It now becomes "When the applied external fields including force, electric, magnetic and optical ones removed, the valleys locked by timereversal symmetry are still degenerate, stabilizing the system in the initial paravalley state.". 11. The sentence "It is known that for representative monolayers of 2H-phase TMDs with trigonal prismatic coordination (D 3h ) 30,31 , such as MoS 2 , the direct band gaps are located at valleys K + and Kwith C 3h point group symmetry." has been replaced by "For representative monolayers of 2H-phase TMDs, such as MoS 2 , they are in trigonal prismatic coordination (D 3h ) 30,31 . The direct band gaps are located at valleys K + and Kwith C 3h point group symmetry.". 12. The sentence "A two-band k·p model neglecting p-orbitals on the chalcogen with |ψ τ u > = |d z 2> and |ψ τ l > = (|d x 2 -y 2> + iτ|d xy >) / 2 (τ = ±1 denotes the valley index) as basis functions can be used to describe the electronic properties near the Dirac points K ± 4,9 ." has been divided into "A two-band k·p model can be used to describe the electronic properties near the Dirac points K ± 4,9 . Noted that the basis functions are chosen as |ψ τ u > = |d z 2> and |ψ τ l > = (|d x 2 -y 2> + iτ|d xy >) / 2 (τ = ±1 denotes the valley index). The p-orbitals on the chalcogen are neglected in the model.".
13. The sentence "According to the total Hamiltonian, the band structures near the valleys K ± of classical TMDs monolayers are easily deduced and schematically drawn in Fig. 1, in which the Fermi level is located at the gap between UB and LB." has been changed to "According to the total Hamiltonian, the band structures near the valleys K ± of classical TMDs monolayers are easily deduced. They are schematically drawn in Fig. 1, in which the Fermi level is located at the gap between UB and LB.".
14. The sentence "While for K -, the one for the bottom of the UB changes as 1E′." has been demonstrated much clearer as "While for K -, they become A′ and 1E′. The IRs for the bottom of UB are different between the two valleys.".
15. The word "split" in the sentence "It is interesting to point out that E opt g excited by the left-handed radiation (E opt g (A + ) = Δ -λ l + λ u + m l -m u ) and the one corresponding to the right-handed light (E opt g (B -) = Δ -λ l + λ u -m l + m u ) split by the magnitude of 2|m lm u |." now has been corrected as "are split".
16. The sentence "Amazingly, inversed chirality of the incident light sees different E opt g in the valley polarized system, indicating the possibility to judge the valley polarization utilizing noncontact and nondestructive circularly polarized optical means." has been replaced by "Amazingly, reversed chirality of the incident light sees different E opt g in the valley polarized system, which indicates the possibility to judge the valley polarization utilizing noncontact and nondestructive circularly polarized optical means.". 17. The sentence "Above discussions establish the general rule to hunt for ferrovalley materials with spontaneous valley polarization, that is the coexistence of the SOC effect with the intrinsic exchange interaction." has been slightly modified as "Above results establish the general rule to hunt for ferrovalley materials with spontaneous valley polarization, i.e. the coexistence of the SOC effect with the intrinsic exchange interaction.".
18. The phrase "following the tactic" in the sentence "Here, following the tactic, we predict a certain material: 2H-VSe 2 monolayer." has been replaced by "following the strategy". 19. The sentence "As a peculiar ferromagnetic semiconductor among TMDs, it possesses intrinsic magnetic moment with the magnitude of 1.01 μ B in the V-3d orbitals, implying remarkable exchange interaction, and then significant spontaneous valley polarization." has been divided into "As a peculiar ferromagnetic semiconductor among TMDs, it possesses intrinsic magnetic moment with the magnitude of 1.01 μ B in the V-3d orbitals. The strong magnetic coupling implies remarkable exchange interaction, and then significant spontaneous valley polarization.". 20. The sentence "More excitingly, on the basis of mean field theory and Heisenberg model, its estimated Curie temperature reaches up to ~ 590 K, in accordance with Pan's work 34 , declaring that it could be used in valleytronics well above room temperature." has been divided into "More excitingly, on the basis of mean field theory and Heisenberg model, its estimated Curie temperature reaches up to ~ 590 K, in accordance with Pan's work 35 . It demonstrates that 2H-VSe 2 monolayer could be used in valleytronics well above room temperature.". 21. The new sentence "Noted that the pristine 1T-phase VSe 2 has been widely studied 37-40 . However, with the presence of space inversion symmetry, it is not a ferrovalley material." has been added to the first paragraph of the subsection "Chiralitydependent optical band gap and Berry curvatures in the ferrovalley material".
22. The sentence "When we ignore the magnetism in monolayer VSe 2 , as shown in Fig.   2a, the band structure is essentially similar to the representative one for TMDs (Fig.   1b), except that it is a metal with the Fermi level passing through the states predominantly comprised of d x 2 -y 2 and d xy orbitals on cation-V." has been split to "When we ignore the magnetism in monolayer VSe 2 , as shown in Fig. 2a, the band structure is essentially similar to the representative one for TMDs (Fig. 1b). Yet, it is a metal with the Fermi level passing through the states predominantly comprised of d x 2 -y 2 and d xy orbitals on cation-V.". 23. The word "Thankfully" in the sentence "Thankfully, the intrinsic exchange interaction of unpaired d electrons, equivalent to a tremendous magnetic field ~ 1.59 × 10 4 T…" has been changed as "Fortunately".
24. The word "Reversely" in the sentence "Reversely, that of primarily d z 2 states is with a relatively greater value at the point K + (|2m u -2λ u | ~ 1.12 eV) than at K -(|2m u + 2λ u | ~ 1.10 eV), due to the opposite sign between λ u and m u ." has been replaced by "Conversely".
25. The sentence "When the magnetic moment is inverted, as clearly displayed in Fig. 2d, our interested valley polarization possess reversed polarity, which causes the red shift of E opt g excited by right-handed light, in comparison to the left-handed one (Fig. 3b)." has been divided into "When the magnetic moment is inverted, as clearly displayed in 26. The word "inversed" in the sentence "Not surprisingly, same value with opposite sign is obtained when the valley polarization has been inversed (Fig. 4d)." has been changed as "reversed". 31. The choice of the PBE functional has been justified as "The exchange-correlation potential is treated in Perdew-Burke-Ernzerhof (PBE) form 48 of the generalized gradient approximation (GGA) with a kinetic-energy cutoff of 600 eV, as others did [34][35][36] . We also check that our results are qualitatively robust within the Ceperly-Alder functional form of the local density approximation (LDA) and taking the Hubbard U into account to describe the on-site Coulomb repulsion between V-d electrons.". The k-mesh used to sample the Brillouin zone now has been stated in our revised manuscript as "A 18×18×1 and 36×36×1 Monkhorst-Pack k-point mesh centered at Γ are respectively adopted in the geometry optimization and selfconsistent calculations.". 32. The meaning of the variables W k , v and c in equation 6, which was not demonstrated in the previous version, has been clearly explained as "The integral over the k space has been replaced by a summation over special k points with corresponding weighting factor W k . The second summation includes v and c states, based on the reasonable assumption that the VB is fully occupied, while the CB is empty.". Some minor changes are not listed here.

Response to Reviewers' Comments (NCOMMS-16-09754A-Z)
- Chen's work), (ii) potential availability -I found some references to experimental VSe2, though not to 2H VSe2 (possibly due to lack of resources as I am travelling).

Thus, after this point is addressed (minor revision) I recommend acceptance.
Answer: We rejoice at the positive recommendation from the reviewer as "after this point is addressed (minor revision) I recommend acceptance". And thank him/her very much for the helpful advice, which definitely improves the quality of our manuscript.
Following his/her suggestions, additional discussion about our material 2H-VSe 2 monolayer has been adopted in our revised manuscript. The stability of monolayer VSe 2 between 1T-and 2H-phase has been definitely pointed out as "In addition, Chen's work 34 proved that compared to 1T monolayer, the ferrovalley 2H one is the slightly more stable phase for single-layered VSe 2 ." in the end of the first paragraph for the subsection "Chirality-dependent optical band gap and Berry curvatures in the ferrovalley material". Especially, Zhongfang Chen's work has been cited here as the reference 34.
When it comes to the potential availability, the 2H-VSe 2 monolayer components were experimentally found in the R polytype VSe 2 bulk. Spiecker et al. (Phys. Rev. Lett. 96, 086401 (2006).) observed T to R polytype transformation in the thin VSe 2 surface layer, which was induced by Cu deposition. Such transformations were also found when electrochemically intercalating Cu into bulk VSe 2 (K. Sollmann. Ph.D. Thesis, Technical University of Berlin, 1995) or intercalating K into VSe 2 in vacuum (Surf. Sci. 461, 137 (2000)). In each single-layer component of the R polytype, the V atoms are in trigonal prismatic coordination with Se atoms, representing a 2H-type monolayer. Based on the reviewer's advice, the sentence "components of which have been already found in the R polytype VSe2 bulk 37 " has been added to our revised version. The experimental work (Phys. Rev. Lett. 96, 086401 (2006).) has been cited here as the reference 37.
We are confident that concerns from the reviewer have been well addressed now. By the way, we would like to take this opportunity to thank him/her for the efforts on improving the quality of our work. Answer: We appreciate that the reviewer acknowledged "the authors made their best effort to answer the reviewers' questions. The work is improved and properly justified".
More importantly, the comments "the power of their method and the immediate interest of other experimental groups demonstrate the importance of authors' work" certainly confirm the novelty and impact of our work. Based on the above and other reviews' recommendation, we believe that our study, which is of both fundamentally physical and practically technological importance in spintronics, valleytronics and crossing fields, is suitable for publication in Nature Communications, and will appeal to a broader audience.